For what values of $d$ can you reduce $d$-coloring polynomially to $d + 1$ coloring?


For what values of $ d$ can you reduce $ d$ -coloring polynomially to $ d + 1$ coloring?

This is a problem that I’ve been thinking about for a while. Assuming 3-Sat and 3-coloring are NP Complete, for what values of $ d$ am I able to polynomially reduce $ d$ -coloring to $ d+1$ coloring and $ d$ -coloring to $ d-1$ coloring?

Thanks